Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction
We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω₀ and a large number 3N of thin rods with thickness of order ε = O(N⁻¹). The thin rods are divided into two levels depending on their length. In addition, the thin ro...
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| Дата: | 2006 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2006
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/178375 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction / T. Durante, T.A. Mel'nyk, P.S. Vashchuk // Нелінійні коливання. — 2006. — Т. 9, № 3. — С. 336-355. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1783752021-02-19T01:27:57Z Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction Durante, T. Mel'nyk, T.A. Vashchuk, P.S. We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω₀ and a large number 3N of thin rods with thickness of order ε = O(N⁻¹). The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The uniform Dirichlet conditions and the nonuniform Neumann conditions are given respectively on the sides of the thin rods from the first level and the second level. Using the method of matched asymptotic expansions and special junction-layer solutions, we construct the asymptotic approximation for the solution and prove the corresponding estimates in the Sobolev space H¹ (Ωε) as ε → 0 (N → +∞). Розглядається мiшана крайова задача для рiвняння Пуассона у плоскому дворiвневому з’єднаннi Ωε, яке є об’єднанням деякої областi Ω₀ та великої кiлькостi 3N тонких стержнiв з товщиною порядку ε = O(N⁻¹). Тонкi стержнi роздiлено на два рiвнi в залежностi вiд їх довжини, i стержнi з кожного рiвня ε-перiодично чергуються. На сторонах тонких стержнiв з першого рiвня задано однорiднi крайовi умови Дiрiхле, а на сторонах стержнiв другого рiвня — неоднорiднi крайовi умови Неймана. З допомогою методу узгодження асимптотичних розвинень та спецiальних розв’язкiв типу примежового шару в зонi з’єднання побудовано асимптотичне наближення для розв’язку даної задачi та доведено вiдповiднi асимптотичнi оцiнки у просторi Соболєва H¹ (Ωε) при ε → 0 (N → +∞). 2006 Article Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction / T. Durante, T.A. Mel'nyk, P.S. Vashchuk // Нелінійні коливання. — 2006. — Т. 9, № 3. — С. 336-355. — Бібліогр.: 22 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/178375 517.956 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω₀ and a large number 3N of thin rods with thickness of order ε = O(N⁻¹). The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The uniform Dirichlet conditions and the nonuniform Neumann conditions are given respectively on the sides of the thin rods from the first level and the second level. Using the method of matched asymptotic expansions and special junction-layer solutions, we construct the asymptotic approximation for the solution and prove the corresponding estimates in the Sobolev space H¹ (Ωε) as ε → 0 (N → +∞). |
| format |
Article |
| author |
Durante, T. Mel'nyk, T.A. Vashchuk, P.S. |
| spellingShingle |
Durante, T. Mel'nyk, T.A. Vashchuk, P.S. Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction Нелінійні коливання |
| author_facet |
Durante, T. Mel'nyk, T.A. Vashchuk, P.S. |
| author_sort |
Durante, T. |
| title |
Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction |
| title_short |
Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction |
| title_full |
Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction |
| title_fullStr |
Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction |
| title_full_unstemmed |
Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction |
| title_sort |
asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/178375 |
| citation_txt |
Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction / T. Durante, T.A. Mel'nyk, P.S. Vashchuk // Нелінійні коливання. — 2006. — Т. 9, № 3. — С. 336-355. — Бібліогр.: 22 назв. — англ. |
| series |
Нелінійні коливання |
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2023-10-18T22:45:22Z |
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2023-10-18T22:45:22Z |
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1796156350680530944 |